Maaser Sheni, Chapter Five, Mishnah Fourteen
This mishnah contains an additional midrash on the verse, And the land which You have given us which was cited in yesterdays mishnah.
1) From here they said that Israelites and mamzerim may make the confession, but not converts, nor freed slaves, since they have no inheritance in the land.
2) Rabbi Meir says: neither do priests and Levites since they did not take a share of the land.
3) Rabbi Yose says: they have the Levitical cities.
Section one: Since the verse states, and the Land which You have given us only those people who received land in the original conquest of Israel can recite the confession. This would exclude converts and freed slaves who did not receive any inheritance in the land of Israel because they were not part of the original 12 tribes. However, it would include Israelites and even mamzerim, for although they were born from an illicit union, they can still trace their lineage to the original twelve tribes.
Section two: Rabbi Meir notes that priests and Levites also did not receive a share of the land, and therefore they too cannot make the confession. The land was divided up to the 12 tribes and Levi is not considered one of the tribes (Josephs tribe is divided into Menashe and Ephraim).
Section three: Although the Levites did not receive a full geographical region, they did receive the Levitical cities (see Numbers 35:1-8). According to Rabbi Yose, this is sufficient for them to be able to recite the tithes confession.